Taking as starting point a Lorentz and CPT non-invariant Chern-Simons-like model defined in 1+3 dimensions, we proceed realizing its dimensional reduction to D = 1 + 2. One then obtains a new planar model, composed by the Maxwell-Chern-Simons (MCS) sector, a Klein-Gordon massless scalar field, and a coupling term that mixes the gauge field to the external vector, v µ . In spite of breaking Lorentz invariance in the particle frame, this model may preserve the CPT symmetry for a single particular choice of v µ . Analyzing the dispersion relations, one verifies that the reduced model exhibits stability, but the causality can be jeopardized by some modes. The unitarity of the gauge sector is assured without any restriction, while the scalar sector is unitary only in the space-like case.

This paper deals with situations that illustrate how the violation of Lorentz symmetry in the gauge sector may contribute to magnetic moment generation of massive neutral particles with spin-1 2 and spin-1. The procedure we adopt here is based on Relativistic Quantum Mechanics. We work out the non-relativistic regime that follows from the wave equation corresponding to a certain particle coupled to an external electromagnetic field and a background that accounts for the Lorentz symmetry violation, and we read thereby the magnetic dipole moment operator for the particle under consideration.We keep track of the parameters that govern the non-minimal electromagnetic coupling and the breaking of Lorentz symmetry in the expressions we get for the magnetic moments in the different cases we contemplate. Our claim is that the tiny magnetic dipole moment of truly elementary neutral particles might signal Lorentz symmetry violation.

We take as starting point the planar model arising from the dimensional reduction of the Maxwell Electrodynamics with the (Lorentz-violating) Carroll-Field-Jackiw term. We then write and study the extended Maxwell equations and the corresponding wave equations for the potentials. The solution to these equations show some interesting deviations from the usual MCS Electrodynamics, with background-dependent correction terms. In the case of a time-like background, the correction terms dominate over the MCS sector in the region far from the origin, and establish the behaviour of a massless Electrodynamics (in the electric sector). In the space-like case, the solutions indicate the clear manifestation of spatial anisotropy, which is consistent with the existence of a privileged direction is space.

The Aharonov-Bohm-Casher problem is examined for a charged particle describing a circular path in the presence of a Lorentz-violating background that is nonminimally coupled to a spinor and a gauge field. The particle eigenenergies were evaluated, showing that the LV background is able to lift the original degenerescence in the absence of magnetic field even for a neutral particle. The Aharonov-Casher phase is used to impose an upper bound on the background magnitude. A similar analysis is accomplished in a space endowed with a topological defect, revealing that both the disclination parameter and the LV background are able to modify the particle eigenenergies. We also analyze a particular case where the particles interact harmonically with the topological defect and the LV background, with similar results.

Recently, a scheme to analyse topological phases in Quantum Mechanics by means of the nonrelativistic limit of fermions non-minimally coupled to a Lorentz-breaking background has been proposed. In this letter, we show that the fixed background, responsible for the Lorentz-symmetry violation, may induce opposite Aharonov-Casher phases for a particle and its corresponding antiparticle. We then argue that such a difference may be used to investigate the asymmetry for particle/anti-particle as well as to propose bounds on the associated Lorentz-symmetry violating parameters.PACS numbers: 11.30. Cp, 11.30.Er, 03.65.Bz The Standard Model of Particle Physics is based on Lorentz-and CP T -invariances as fundamental symmetries that have been confirmed in numerous experiments [1]- [5]. Actually, the invariance under the combined CP Ttransformation is a consequence of first principles of relativistic quantum field theory. The most immediate consequence of CP T symmetry is the equality of mass and lifetime for a particle and its corresponding antiparticle. The best tests in this direction come from the limits on the mass difference between K 0 and K 0 [3], high precision measurements of the anomalous magnetic moments of the electrons, positrons and mesons (confined in a Penning trap) [4], and clock-comparison experiments [5].Lorentz-violating theories are presently studied as a possible extension of the Standard Model of Particle Physics. This proposal has been pushed forward by Colladay and Kosteletcký [6], who devised a Standard Model Extension (SME) incorporating all tensor terms stemming from the spontaneous symmetry breaking of a more fundamental theory. In this case, an effective action breaks Lorentz symmetry at the particle frame, but keeps unaffected the SU (3) × SU (2) × U (1) gauge structure of the underlying fundamental theory. This fact is of relevance in that it indicates that the effective model may preserve some good properties of the original theory, like causality, unitarity and stability.In the context of gauge theories endowed with Lorentz violation, some efforts have been recently devoted to investigate interesting features of relativistic quantum-mechanical models involving the presence of fermions. Indeed, considering the Dirac equation enriched by of a sort of non-minimal coupling, significant consequences on the particle behavior has been observed, as pointed out in the works of ref. [7]. In these papers, the analysis of the non-relativistic regime of the Dirac equation has revealed that topological quantum phases are induced whenever the fermion field is coupled to the fixed background and the gauge field in a non-minimal way. More specifically, it has been found out that a neutral particle acquires a magnetic moment (induced by the background), which originates the Aharonov-Casher (AC) phase subject to the action of an external electric field [10]. It is worth stressing that the standard Aharonov-Casher phase is interpreted as a Lorentz change in * Electronic address:

In this work, we present two possible venues to accomodate the KF -type Lorentz-symmetry violating Electrodynamics in an N = 1-supersymmetric framework. A chiral and a vector superfield are chosen to describe the background that signals Lorentz-symmetry breaking. In each case, the K µνκλ -tensor is expressed in terms of the components of the background superfield that we choose to describe the breaking. We also present in detail the actions with all fermionic partners of the background that determine K µνκλ .

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